What is the integral of (sin(y)-ysin(x)) ?

The integral of (sin(y)-ysin(x)) is xsin(y)+ycos(x)+C

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integral of (sin(y)-ysin(x))

\int (sin (y) - y sin (x)) d x

x sin (y) + y cos (x) + C

Solution steps

\int sin (y) - y sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (y) d x - \int sin (x) y d x

\int sin (y) d x = sin (y) x

\int sin (x) y d x = - y cos (x)

= sin (y) x - (- y cos (x))

Simplify

= x sin (y) + y cos (x)

Add a constant to the solution

= x sin (y) + y cos (x) + C

\frac{\partial}{\partial t} (x + y sin (t))

\frac{d}{d x} (x^{2} + c^{2})

\frac{d}{d x} (\frac{2}{2 + x})

\frac{\partial}{\partial y} (3 x^{2} - 12 y)

y = (\frac{x + 1}{x - 1})^{2}, (3, 4)

What is the integral of (sin(y)-ysin(x)) ?
The integral of (sin(y)-ysin(x)) is xsin(y)+ycos(x)+C